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Algebra 1 Skills Needed tobe Successful in Algebra 2

A. Simplifying Polynomial ExpressionsObjectives: The student will be able to:

Apply the appropriate arithmetic operations and algebraic properties needed tosimplify an algebraic expression.Simplify polynomial expressions using addition and subtraction.Multiply a monomial and polynomial.

B. Solving EquationsObjectives: The student will be able to:

Solve multi-step equations.Solve a literal equation for a specific variable, and use formulas to solve problems.

C. Rules of ExponentsObjectives: The student will be able to:

Simplify expressions using the laws of exponents.Evaluate powers that have zero or negative exponents.

D. Binomial MultiplicationObjectives: The student will be able to:

Multiply two binomials.

E. FactoringObjectives: The student will be able to:

Identify the greatest common factor of the terms of a polynomial expression.Express a polynomial as a product of a monomial and a polynomial.Find all factors of the quadratic expression ax + bx + c by factoring and graphing.

F. RadicalsObjectives: The student will be able to:

Simplify radical expressions.

G. Graphing LinesObjectives: The student will be able to:

Identify and calculate the slope of a line.Graph linear equations using a variety of methods.Determine the equation of a line.

H. Regression and Use of the Graphing CalculatorObjectives: The student will be able to:

Draw a scatter plot, find the line of best fit, and use it to make predictions.

Graph and interpret real-world situations using linear models.

A. Simplifying Polynomial Expressions

I. Combining Like Terms

You can add or subtract terms that are considered "like", or terms that have the same

variable(s) with the same exponent(s).

Ex. 1:

Ex. 2:

5x - 7y + IOx + 3y

lox + u

15x - 4y

-8h 2 + 10h3 - 12112 - 15h3

3

-20112 - 5h3

Il. Applying the Distributive Property

Every term inside the parentheses is multiplied by the term outside of the parentheses.

Ex. 1: Ex. 2: 4x2 (5x3 + 6x)

3-9x-3•4

27x-12

4x 2 • 5x3 + 4x 2 • 6x

20x 5 + 24x3

Ill. Combining Like Terms AND the Distributive Property (Problems with a Mix!)

Sometimes problems will require you to distribute AND combine like terms!!

Ex. 2:

3•4x-3-2+13x

12x-6+ 36x-15+63-90x

25x-6 — 54x + 48

5

PRACTICE SET 1

Simplify.

l. 8x—9Y+ 12y

16x -1-3

3. 5n—(3 —4n)

5. IOq(16x+11)

IIO

7. 3(18z — 4w) + 2(10z —6w)

'71-1 -L w

2. 14Y+22-15y 2 +23y

— 16

4. -20 lb -3)

6. —(5x — 6)

8. (8c +3) +12(4c -10)

6010. -(y -x) + 7)

6

B. Solving Equations

I. Solving Two-Step Equations

A couple of hints: l. To solve an equation, UNDO the order of operations and work

in the reverse order.

2. REMEMBER! Addition is "undone" by subtraction, and vice

versa. Multiplication is "undone" by division, and vice versa.

Ex. 1: 41-2=30 Ex.2: 87=-11x+21

4x = 32

+4 +4

-21 -21

66 = —l Ix

11 *-11

Il. Solving Multi-step Equations With Variables on Both Sides of the Equal Sign

When solving equations with variables on both sides of the equal sign, be sure to get

all terms with variables on one side and all the terms without variables on the other

side.Ex. 3: 8x+4= 4x + 28

—4 —4

8x 4x + 24

4X = 24

Ill. Solving Equations that need to be simplified first

In some equations, you will need to combine like terms and/or use the distributive

property to simplify each side of the equation, and then begin to solve it.

Ex. 4: 8X + 45 + 2X

20x-35=10X+45

-lox -lox

lox-35=45+35 +35

lox = 80

+10 +10

7

PRACTICE SET 2

Solve each equation. You must show all work.

1. 5x-2=33

355 5

3. 8(3x — a) = 196

& 31

9.55. 4(12x -

131=

—131 1— 90

-Ill9. 121 +8 - 15 = -2(3x - 82)

9.5IV. Solving Literal Equations

4x + 36

I o QC

10 x4. 45x—720 + 15x = 60

60 60x z 13

6. 198=154+71-68-—15k

x8. -71-10=18+3x

10 —3X

— 10 —to

10.

x

A literal equation is an equation that contains more than one variable.You can solve a literal equation for one of the variables by getting that variable by itself(isolating the specified variable).

Ex. l: 3xy = 18,

3xy 18

3y — 3y

6

Ex.2: 5a-10b= 20, Solve for a.Solve for x.

+10b = + 10b

5a = 20 +10b

20 10b

5 5 5

a = 4 +2b

8

PRACTICE SET 3

Solve each equation for the specified variable.

1. Y+V=W, for V

3. 2d-3f= 9, forf__q +34

201-9

5. )180, forg

Ito

= 81, for w

4. dx+t— 10, for x

-z lo-t

6. —1 + u, for x

-7+5 k

9

C. Rules of Exponents

Multiplication: Recall (xmEx: (3x y2

(m+n) 4 ) =

xDivision: Recall (m—n)

x

Powers: Recall (xm y = x(m•n)

Power of Zero: Recall xo = 1, x

PRACTICE SET 4

Simplify each expression.

8c c

7. (-t 7 )3

12a4b610.

36ab 2c 3 C

13.

Ex:

Ex:

42m5J2

— 3m3j

42

—3

0

2.

5.

8.

ll.

14.

15m

3m

Ex:

3f3go

3

(3m2n)4

(—2a 3 bc 43 ) =

5xoy4 =

.2

.1)

2= —14m j

1343 9 b

3 c

12) (c ) = —8a

= 5y4

1.105

3.

45j'3z106.

5y3z

9.

GO

12. (12x 2 y) 0

15.

LIX

10

D. Binomial Multiplication

I. Reviewing the Distributive Property

The distributive property is used when you want to multiply a single term by an

expression.

Ex 1: 8(5x — 9x)

8•5x + 8 (—9x)

401 - 721

Il. Multiplying Binomials — the FOIL method

When multiplying two binomials (an expression with two terms), we use the

"FOIL" method. The "FOIL" method uses the distributive property twice!

FOIL is the order in which you will multiply your terms.

First

Outer

Inner

Last

Ex. 1: (x +

FIRST

(X +

INNER

10)

OUTER

+ 10)

LAST

First

Outer

Inner

Last

x•10

6•10

x2 + lox + 6x+ 60

2

-> 10x

> 6x

> 60

x2 + 16x+ 60(After combining like terms)

11

Recall : 42 =4-4

x

Ex. (x+

PRACTICE SET 5

Multiply. Write your answer in simplest form.

Now you can use the "FOIL" method to geta simplified expression.

X + x—OtO

X —l ox + to

5. ( - l)ßx+ )+ -- 53—3

7. x-4)Gx+ )

9. (_x + 5)2ee (

x 1 — +2-5

X —lox

2. ( + ) x— 12)

X —5x-8k

6. (- + Ux+5)

—lox—hox +50I tx —100* +50

X 100

10. (2x-3) 2

12

3/28/2017

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Hou to Factor Polynomials Easily

CnAnrStay connected

How to Factor PolynomialsLearning how to factor polynomials does not have to be difficult. GradeA willbreak down the steps for you, show you simple examples with visual illstrations,and also give you some clever tips and tricks.

Use the followina steps to factor your polynomials:

1) Take out the GCF if possible

* Learn how to factor out a GCF

2) Identify the number of terms

More information about terms

* 2 term factorinq techniques

* 3 term factoring techniques

3) Check by multiplying

Check with Math FOIL system

Do you want to know how to solve quadratic equations (ex: x2 + 8x+ 15 = 0)?Learn how to solve quadratic equations, which is a different type of problem thanfactoring, so it requires a different process.

Factoring Binomials: The Differece of Two Squares

Remember, make sure to always factor outa GCE first. Sometimes that's the only partof the binomial that can be factored. Onceyou have checked for the GCF, then you canmove forward to solving the problem:

If you are taking a basic algebra class, you probably only need to know one typeof factoring when you have two terms: its called the difference of two squares.You need to know how to factor the difference of two squares if you want toknow how to factor polynomials.

2 — 16

x2 is a "square" because it =

x 16 is a "square" because it = 4-4

square #1 minus square #2

The example shown above is very common factoring problem. It is called thedifference of two squares because it is a subtraction problem ("difference"indicates subtraction) and they are perfect squares between there is somenumber times itself that gives you that number. MQr.g-a.ÄQUt-EEf-e-C,t-S.AUa.C-eS.

Here are a few more examples of difference of two squares:

x2 - 25 4x2 — 49 9x2 - 36

Now, onto the factoring..

S.tep_l: Find the square root of each term.

Ste.2_2•. Factor into two binomials - one plus and one minus.

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